System and method for high throughput fractionated satellites (HTFS) for direct connectivity to and from end user devices and terminals using flight formations of small or very small satellites

ABSTRACT

A high throughput fractionated satellite (HTFS) system and method where the functional capabilities of a conventional monolithic spacecraft are distributed across many small or very small satellites and a central command and relay satellite, the satellites are separated and flight in carefully design formations that allows the creation of very large aperture or apertures in space drastically reducing cost and weight and enabling high throughput capabilities by spatially reuse spectrum.

RELATED APPLICATION

This application is a continuation-in-part of U.S. patent applicationSer. No. 15/979,298, filed May 14, 2018, which is a continuation of U.S.patent application Ser. No. 15/675,155, now U.S. Pat. No. 9,973,266,filed Aug. 11, 2017, which claims priority to India ProvisionalApplication No. 201711020428, filed Jun. 12, 2017. The entire contentsof those applications are incorporated herein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a high throughput fractionatedsatellite (HTFS) system and method where the functional capabilities ofa conventional monolithic spacecraft are distributed across many smallor very small satellites and a central command and relay satellite. Thesatellites are separated and fly in design formations that allow thecreation of very large aperture or apertures in space. The aperturegenerally refers to the area of an antenna and relates to the ability ofthe antenna to receive and transmit signals. As the aperture increases,the effectiveness of the antenna in receiving, transmitting anddirectionality of signals also increases.

Furthermore, LEO satellites generate prodigious Doppler at the edge oftheir field-of-view (FOV) depending on their velocity and the carrierfrequency. In a communication system comprising low-cost user equipment(UE) and a Ground Station (GS), this Doppler can be compensated eitherat the satellite or in GS equipment depending on the geo-location of theUE, the satellite ephemeris, the geo-location of the GS, the carrierfrequencies for UE-to-satellite linking and the carrier frequencies forGS-to-satellite linking. It is advantageous to correct Doppler to abeam-center rather than each UE individually; however, this results in adifferential Doppler depending on the beam-diameter. The smaller a beam(the larger the aperture), the smaller the differential Doppler. Thusthe size of the aperture is also dictated by the maximum differentialDoppler that the UE-to-Base Station (in satellite case, UE to GS)communication system can tolerate.

More particularly, the present invention relates to an array system ofsmall or very small satellites and a central command and relaysatellites. The array of small or very small satellites are coordinatedto act as a large aperture in space. This reduces weight and powerrequirements and results in a drastic reduction in cost and drasticimprovement in aperture gain and bandwidth reuse performance. Satellitescan be partially connected or structurally unconnected and keep in closeproximity using electromagnetic forces, solar forces and other naturalorbit related forces aided by GPS systems and positioning.

Background of the Related Art

Present antennas are monolithic and are either fed power via a parabolicreflector or comprise phased arrays of many antenna elements. In both ofthese cases, the antenna aperture is structurally one and limited insize to typically few square meters. The main issues with deployment oflarge antenna structures in space are twofold. First, cost and weightdrastically increase with size due to the cost of launching large andheavy objects into space. And second, any pre-fabricated structure(including deployment mechanisms and support structures) must withstandlarge accelerations at launch and its strength has to be designed totake into account these forces rather in than the micro-gravityoperating environment.

Spacecraft component weight and cost are related to the required payloadpower of a particular satellite mission. Payload power requirements aremostly driven by end user terminals required to target Signal to Noiseratio, number of simultaneous users and channel bandwidth requirements.As the payload power requirement increase the RF components, batteries,solar panels and other power handling components on the satellite alsoincrease in weight and cost. In addition, as end user devices andterminals (such as handheld devices, very low power terminals likemodern smartphones, geo location bracelets, radios, telephones,cellular, smart phones, loT terminals, and bracelets for tracking peopleor machine tracking devices, collectively referred to herein as “enduser devices” or “end user terminals”) become smaller and lighter, theirtransmitting power and directionality require larger apertures in spacein order to enable direct connectivity from and to those end userdevices and terminals.

State of the art LEO communications satellites designed to connectdirectly to end user devices like satellite phones or low power IOTdevices, weigh between 500 to 1,000 kg and are costly to build andlaunch.

SUMMARY OF THE INVENTION

One object of the present invention is to provide a distributed aperturesystem having the capabilities of a large or very large antenna deployedin space ranging but not limited from 25 m² to 300,000 m² in aperturesurface. Another object of the invention is to provide an aperturesystem in space that minimizes or entirely reduces pre-fabricatedstructure. In accordance with these and other objects, the presentinvention includes an array of very small or small satellites,coordinated to act as a large aperture, but that are partially connectedor structurally unconnected.

There are several advantages to this approach. First, the interstitialmass of connecting elements is eliminated, reducing satellite launchweight, and hence launch cost. Second, very large apertures can berealized in space and this is of particular advantage in realizing highantenna efficiencies at relatively low frequencies. And third, bandwidththat is scarce and expensive can be re-used spatially more than tens ofthousands of times, thereby enabling high throughput capabilities byrealizing narrow-beams and beam forming using distributed signalprocessing algorithms at both the small and very small satellites andthe control and relay satellites.

The HTFS equivalent antenna aperture drastically increases in size dueto the use of a distributed satellite aperture. As a result, therequired size for RF components, batteries, solar panels and powerhandling components is drastically reduced in size or is eliminated, asin the case of waveguide systems of monolithic satellites. This alsodrastically reduces the weight and cost required for the satellitesystem.

Another benefit is the reduction on the required power levels by eachdiscrete satellite. The HTFS architecture of the present inventionutilizes commercial of the shelf components that are built in millionsof units for consumer electronics. Critical components required in HTFSsystem like Software define radios, HPA, LNA and Filters then becomeavailable as commercial of the shelf components already optimize forweight and cost.

HTFS systems described in this invention, when compared with monolithicsatellites, require a fraction (approximately one-tenth) of the weightcompared to a monolithic satellite for an equivalent number of end usersand similar bandwidth requirements. For example, an equivalentcapability monolithic satellite that weighs 1,000 kg can be constructedusing a HTFS according to the present invention with a collective weightof approximately 100 kg, providing a drastic reduction in weight andcost.

The HTFS system described in this invention creates an equivalent verylarge distributed aperture provides great benefit on cost, weight andSpectrum re-use. These benefits are particularly obvious for spectrumbetween 100 MHz and 2 GHz typically use for direct connectivity to enduser terminals. The low frequency spectrum (e.g., between 100 MHz to 2GHz) is particularly good for eliminating the use of antennas, gatewaysor VSAT systems between the end user and the HTFS systems in space.Loses caused by buildings, trees, airplane fuselage, train, car andvessels structures and other obstructions to the line of sight getreduce as compared to higher frequency systems like V, Ka, Ku, C, X. Inaddition, costly and heavy satellite tracking system at end userterminals required on higher frequency spectrum are eliminated at lowerband frequencies. Also, low band frequencies connecting to an HTFSsystem of the present invention allow end user devices to connectdirectly to the HTFS system without VSAT terminals or costly and heavytracking antennas enabling numerous aplications and usage for thisinvention.

These and other objects of the invention, as well as many of theintended advantages thereof, will become more readily apparent whenreference is made to the following description, taken in conjunctionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES

FIGS. 1(a), (b) show the satellite communication system in accordancewith the preferred embodiment of the invention

FIGS. 2(a) and 2(b) are block diagrams of the system of FIG. 1;

FIG. 3 shows the noise temperature in a single-channel receiver;

FIG. 4 is a general array receiving system for each small satellite 302and for the satellite array 300 as a whole;

FIGS. 5(a), (b), (c) show the communication footprints on Earth and beamswitching;

FIG. 6 shows an alternative arrangement of small satellites in an arrayhaving a trapezoidal configuration;

FIG. 7(a) shows the formation entering the footprint for the array ofFIG. 6;

FIG. 7(b) shows the formation in the middle of the footprint for thearray of FIG. 6;

FIG. 7(c) shows the formation leaving the footprint for the array ofFIG. 6;

FIGS. 8(a), 8(b), 8(c) show beam switching;

FIGS. 9(a), 9(b) show radiation patterns;

FIG. 10 shows the footprint cell frequency layout; and

FIG. 11 is a block diagram of a ground station having Dopplercompensation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In describing the preferred embodiments of the present inventionillustrated in the drawings, specific terminology is resorted to for thesake of clarity. However, the present invention is not intended to belimited to the specific terms so selected, and it is to be understoodthat each specific term includes all technical equivalents that operatein a similar manner to accomplish a similar purpose.

Turning to the drawings, FIG. 1(a) shows the satellite communicationsystem or HTFS 100 in accordance with one exemplary, illustrative,non-limiting embodiment of the invention. The satellite system orsatellite formation 100 includes a plurality of small or very smallelements such as small or very small satellites 302 (e.g., slave orremote satellites) and a local controller and relay satellite 200 (e.g.,master or central satellite, also referred to here as the controlsatellite). The satellites 302 can be any suitable satellite such as forexample, altitude-controlled very small satellites 302 that are verysmall in size and can be lightweight (e.g., <1.5 Kg in weight). As analternative, many antenna elements may be integrated into a singleassembly, the advantage of this being that some of the interstitialspacing between elements can also be used by solar cells in order toenhance power available to those elements. For example, as shown, eachremote satellite can have a housing 304 that houses four antennas 305that can be electrically connected together by a wire. For ease ofillustration, only three remote satellite housings 304 are shown in FIG.1(a).

The remote satellites 302 are operated in Low Earth Orbit (LEO). Thesmall satellites 302 operate below the Van Allen belt of plasma at 700km/1400 km because operating above the Van Allen Belt requires moreexpensive space-hardened components. However, the invention is notlimited to operate in any particular orbit or combination of orbits, andother suitable orbits can be utilized on all LEO, MEO and GEO orbits,including above the Van Allen Belt.

The system 100 (including the central satellite 200 and the smallsatellites 302) has two primary configurations: an operatingconfiguration, and a shipping or storage configuration. In the operatingconfiguration, a plurality of the small satellites 302 are formedtogether in space to form an array 300. In one example embodiment,one-thousand (1,000) small satellites 302 are provided, though anynumber of small satellites 302 can be provided, including substantiallygreater or fewer than 1,000. The array 300 forms a very large spatialarray 300. In the example embodiment of 1,000 small satellites 302, thearray 300 can be over 500 meters in width and/or height. In the arrayconfiguration, the small satellite 302 antennas are equivalent to alarge antenna that enhances communication with the Earth. The remotesatellites 302, in essence, are fractionated in that they provide adistributed phased-array antenna, rather than a monolithic or connectedarray.

Also in the operating configuration, the array 300 is formed about thecentral satellite 200. The array 300 is positioned and configured toface the Earth. That is, the array 300 defines a top surface that can belinear or curved, and that top surface generally faces the Earth. Thelarger satellite 200 is positioned substantially at the centre of massof the array 300 formation. The small satellites can be positionedapproximately a few centimetres to approximately 20 meters apart fromeach other.

In addition, the system 100 and the small satellites 302 can be placedin a storage or transport configuration. The small satellites 302 areseparate discrete devices and are not physically connected to oneanother. The small satellites 302 can be consolidated or combinedtogether for storage and transportation and then formed into the largesatellite array 300 in space. For example in the shipping configuration,multiple small satellites 302 can be placed together in a singleshipping container such as a box, for transport on a rocket or othertransport device or space craft. Once the shipping container(s) reachesa release position in space at a desired orbit, the shipping containercan be opened and the small satellites 302 can be released. The smallsatellites 302 can then automatically manoeuvre by themselves and/orwith the assistance of the control satellite 200, to enter into theoperating configuration array in space. The central satellite 200 can bealready positioned in space. Or the central satellite 200 can betransported in a separate shipping container and separately positionedin space either before or after the array 300 is formed.

This reduces the space required by the small satellites 302 duringtransport, but enables the small satellites 302 to form a large arraywhen in the operating configuration. The small satellites 302 can takeup a space of a few square meters depending on the number of satellites302, which converts to many square meters when deployed in space. Thisalso substantially reduces the complexity of the array 300 and thelaunch mass because structural members are not needed to connect thesmall satellites 302 to each other or to the controller satellite 200 inthe operating configuration. Thus, the satellite array 300 can be formedwith minimal human intervention (such as to release the satellites 302from the shipping container and space craft), and can even be formedwithout any physical human intervention (such as to build a frame orother structure for the array). In addition, multiple arrays 300 can beprovided at various locations in space to form a constellation ofsatellite arrays 300 to obtain full communication coverage of Earth. Forinstance, approximately 50-100 arrays 300 located at LEO orbits can beprovided to obtain complete continuous coverage of Earth.

It should be noted that the remote satellites 302 can be moved andpositioned in any suitable manner. In one embodiment shown in FIGS.2(a), 2(b), the remote satellites 302 and central satellite 200 areprovided with impulse actuators such as one or more electromagneticcoils 314 and with magnetorquers 316 to move the remote satellites 302.

In more detail, FIG. 2(a) is a block diagram of the small or very smallremote satellites 302. The remote satellites 302 include a processingdevice 306, radio transceivers 308 in communication via an antenna 310,a GPS 312, electromagnetic coils 314, magnetorquers 316, electricalpower management 320, heat sink 322, solar power 324, and battery power326. The remote satellite 302 components are divided in two parts, thoserelated to energy management and those related to the use of the energy.The electrical power is obtained from different sources like heat, lightor chemical. These components are the heat sink 322, the solar power 324and the battery power 326, respectively. Communications between remotesatellites 302 or between a remote satellite 302 and the centralsatellite 200 are done by the radio transceiver 308 and the antenna 310.

FIG. 2(b) is a block diagram of the electromagnetic system formaintaining a constant relative position between the remote satellites302 and between the remote satellites 302 and the central satellite 200.Referring to FIGS. 2(a) and 2(b), satellite positioning is done in termsof distance x and angle y. The onboard computer or processing device 306computes the required maneuvers to maintain a predetermined ordynamically-determined desired (which can be variable or random)distance x and angle y for the remote satellite 302 with respect theother remote satellites 302 and with respect to the central satellite200. It does this by comparing the relative position of the remotesatellite 302 with the other remote satellites 302 and with the centralsatellite 200. The electromagnetic coils 314 generate electromagneticforces to gain movement by changing the relative distance between theremote satellite 302 and other remote satellites 302 or between theremote satellite 302 and the central satellite 200. It is noted thatFIG. 2(b) shows the distance and angle between the remote satellites 302and the central satellite 200. It will be appreciated that the distanceand angle is also maintained between the remote satellites 30themselves, in the same manner.

The magnetorquer 316 generates rotations around the satellite center ofmass to control the angle y with respect to other remote satellites 302or with respect to the central satellite 200. The global positioningsystem 312 compares the relative satellite position with respect to theglobal position.

The central satellite 200 is the reference of the satellite array and ithas to know its global position via the GPS 202, but it does not need toknow its relative position. Thus, the central satellite 200 does not usemagnetorquers (as in the remote satellites), only electromagnetic coils204. The electromagnetic formation flight system maintains the desireddistance x and the desired angle y between each small satellite 302and/or the central satellite 200, by generating electromagnetic forcesand/or rotations. The electromagnetic coils 314 control the distance xby comparing its position with respect to the one obtained from theGlobal Positioning System 312.

It will be recognized, however, that the GPS 312 is optional in theremote satellite 302. The central satellite 200 includes a GPS 202,which means that the remote satellites 302 only need to know itsrelative position to the neighboring and/or surrounding remotesatellites 302 and the relative position between that remote satellite302 and the central satellite 200. However, one or more of the remotesatellites 302 in the array 300 can use the GPS 312 to determine itsglobal position to further facilitate positioning of the remotesatellite 302. In that instance, it is possible for the GPS 202 of thecentral satellite to be omitted and the central satellite 200 to onlyuse its relative position to one or more of the remote satellites 302.

The magnetorquers 316 control the angle y by measuring the relativeposition. The corrections are done through a number of maneuvers untilthe position and the angle are stable. Then corrections are onlyrequired when any disturbance occurs like high charged particles (i.e.,cosmic ray, Van Allen belt charged particles, etc.) impacting to aparticular satellite. The solar wind, the orbit rotation or theinteraction between satellites are not considered disturbances becausethey are predictable and are part of the maneuvers.

It is noted that electromagnetics are used to maintain the distancebetween remote satellites 302 within an operating range and between theremote satellites 302 and the control satellite 200 within an operatingrange. However, the invention also makes use of first ordergravitational forces between the remote satellites 302 and Earth andbetween the control satellite 200 and Earth, as well as due to thenatural orbit of the remote satellites 302 and the control satellite200. The invention positions the remote satellites 302 and the controlsatellite 200 to make use of that gravitational force and minimize theamount of positioning that has to be done by using the electromagneticsor other outside forces. In addition, the gravity forces create an orbitfor the satellites 302, 200. The invention uses the natural orbit of thesatellites 200, 302 to maintain the position of the remote satellites302 in the array 300, as well as the position of the control satellite200 with respect to the remote satellites 302. Finally, the array 300and control satellite 200 naturally rotates, and the array 300 andposition of the satellites 200, 302 are configured to account for thenatural rotation and minimize positional adjustments of the satellites200, 302 needed due to that rotation. For example, an algorithm can beutilized by the control satellite 200 to dynamically adapt to volumetricshape rotation of the remote satellites 302, and/or to dynamically adaptto relative position of the remote satellites and the target beam objector geography. That algorithm can account for gravitational forces, thenatural orbit, and rotation.

FIGS. 1(a), 1(b), 2(a), 2(b) are block diagrams of the system 100showing central satellite 200 to very small satellites 302communications via wireless communication network. The remote satellites302 include a remote controller 304 (e.g., processor or processingdevice) with a control interface, antenna 305, and a transmitter and/orreceiver. The transmitter/receiver communicate with the controllersatellite 200 such as via wireless communication network. The satellites302 are solar-cell powered and have a chargeable capacitor or batteryfor eclipses or the like.

The satellites 302 can include an avionic system that includeselectromagnetics or the like to position the satellites 302 in the arrayformation that is controlled by the controller 304. The avionic systemmaintains the satellite 302 at the proper altitude, location andorientation, such as to maximize communications with devices on theEarth and the communication footprint and also to maintain thesatellites 302 together in an array 300 formation. The remote satellite302 can also communicate with other remote satellites 302 to achieve theproper avionics.

Electromagnetic forces are utilized between the small remote satellites302 and the control satellite 200 to keep the remote satellites 302 information and alignment and for distribution of power. The additionalmass associated with the generation of magnetic forces is much lowerthan the mass of structural connections between elements and,potentially, their deployment mechanism.

The central controller satellite 200 is provided for each array 300. Inone embodiment, the controller satellite 200 can be a CubeSat or a smallsatellite. The controller satellite 200 communicates with each of thesmall satellites 200. For example, the controller satellite 200 can havea central controller (e.g., processor or processing device) thatcommunicates with the remote controller 304 of each of the remotesatellites 302. The central controller can control operation of theremote satellites 302 via remote controller 304, such as during normalcommunications between the central satellite 200, the remote satellites200, and the ground station, and can implement commands to the remotesatellites 200 that are received from the ground station. The centralcontroller can control formation of the remote satellites 302 into thearray 300. The central controller can also position the centralsatellite 200 to avoid electromagnetic shading or occlusion by the array300 and to control communication frequencies during deployment andoperation.

The remote satellites 302 can be of any shape. In addition, thesatellite array 300 is either square, rectangular, hexagonal or circularin shape, with the remote satellites 302 aligned with each other in rowsand columns, whereby the array is a two-dimensional array (i.e., therows and arrays are in an x- and y-coordinate). The remote satellites302 are controlled to be spaced apart from each other by a predetermineddistance (or in an alternative embodiment, the distances can vary foreach remote satellite 302 and can be dynamically controlled the remotesatellite 302 and/or control satellite 200). However, any suitable sizeand shape can be provided for the satellites 302 and the satellite array300, as well as for the spacing, and the array can be three-dimensional.

Referring to FIG. 1(b), the communication scheme is shown. The end userterminal 500 communicates with a multitude of satellites 302 via a sub 2Ghz frequency. This frequency is called the Tx end user frequency. Asshown, and as more fully discussed with respect to FIG. 10 below, theground footprint cells each communicate on one of four differentfrequencies. That is, the end user terminal 500 in a first footprintcell communicates at a first frequency F₁, the end user terminal 500 ina second footprint cell communicates at a second frequency F₂, the enduser terminal 500 in a third footprint cell communicates at a thirdfrequency F₃, and the end user terminal 500 in a fourth footprint cellcommunicates at a fourth frequency F₄. Thus, the frequencies F₁-F₄ arereused multiple times (i.e., to communicate with end user terminalslocated in multiple different footprint cells), which enables a highthroughput bandwidth. Multiple end user terminals 500 that are locatedin the same cell (e.g., the first footprint cell), can communicate overthe same frequency (i.e., the first frequency F₁) by use of timedivision multiplexing or other suitable transmission scheme.

The multitude of satellites 302 and the control satellite 200 form aWIFI wireless network to communicate between them in order to aggregatethe satellite 302 receive signals at the control satellite 200 and toaid the positioning satellite system. As shown, there can be multiplecontrol satellites 200 that communicate with each other or with a givenarray 300. The control satellite 200 communicates with a gateway 600(which for example can be located at a ground station on Earth) via ahigh frequency like KA band or V Band, which in turn communicates withthe Internet, cellular systems or a private network (such as via a fiberoptic link or other link). This frequency is call downlink gatewayfrequency. The gateway 600 communicates back to the control satellite200, also via a high frequency. This frequency is call uplink gatewayfrequency.

The control satellite 200 and the multitude of satellites 302 form aWifi wireless network to communicate between them. Thus, the controlsatellite 200 can distribute signals to different small satellites 302in such a way that transmit signals to the Earth generate specific beamforming 400 on the Earth field of view. The multitude of smallsatellites 302 transmit back to the end user devices 500. This frequencyis called the RX end user frequency, and can be a low frequency. The F₁Rx is the same band, but different frequency as F₁ Tx. The same transmitfrequency is reused in multiple cells—that is, F₁ Tx is the same in eachof the multiple F₁ cells, and the F₁ Rx is the same in each of themultiple F₁ cells; and F₄ Tx is the same in each of the multiple F₄cells, and the F₄ Rx is the same in each of the multiple F₄ cells, etc.

The main frequencies are the transmit end user frequency Tx, the receiveend user frequency Rx, the network (between the remote satellites 302and the central satellite 200) frequency, the downlink gateway frequencyand the uplink gateway frequency. The end user frequency Tx for examplecan be the LTE band 31. The Rx end user frequency can be the LTE band31. The WiFi AC network frequency can be 5 GHz. The downlink gatewayfrequency can be the Ka band. And, the uplink gateway frequency can bethe Ka band uplink.

Thus, the Up- and Down-links between the controller satellite 200 andthe ground gateway (located on Earth) is via a high-frequency, and thesystem can be designed to communicate to other satellite systems inspace over different communication bands in order to reduce the numberof gateways required on Earth. Thus, the satellites 302 communicate withthe end user device or terminals in low-frequencies and with the centralsatellite 200 via wireless communication network equivalent to WiFi. Thesystem is capable of operating in Low Frequency connecting user devicesand user terminal directly from and to the array 300 using lowfrequencies preferred for Moderate Obstacle Loss. Examples of frequencybands within the range of 100 MHz-2 GHz.

The G/T and EIRP (Equivalent Isotropic Radiated Power) of thedistributed antenna system array in Space determines the number of bitsper Hertz, frequency reuse and required power in each small or verysmall satellite. In order to derive this, FIG. 3 shows the noisetemperature in a single-channel receiver. The following derives theantenna array's G/T of the satellite array 300 from a single channelreceiver model.

FIG. 4 is a general array receiving system for each small satellite 302and for the satellite array 300 as a whole. The signal power atbeam-forming network's output is:

$S_{o} = {P_{o}G_{m}{{\sum\limits_{n = 1}^{N}{( \sqrt{G_{en}} )a_{n}{\exp( {j\;\theta_{n}} )}}}}^{2}}$where P_(o) is the lossless isotropic antenna's power output, G_(en) isarray antenna element gain, G_(n) is available gain of a channel fromthe output of the n-th antenna element to the beam former output, G_(m)is the maximum value of G_(n), used for normalization anda_(n)=Sqrt(G_(n)/G_(m)) is the effective amplitude taper of the n-threceiver channel transfer function. θ_(n) is the total phase shift ofthe n-th receiver channel with respect to that of the reference channel,accounting for beam steering and/or a phase taper.

Substituting the power gain of an array antenna

$G_{a} = {{{\sum\limits_{n = 1}^{N}{( \sqrt{G_{en}} )a_{n}{\exp( {j\;\theta_{n}} )}}}}^{2}/{\sum\limits_{n = 1}^{N}a_{n}^{2}}}$in the above equation, we get

$S_{o} = {P_{o}G_{a}{\underset{n = 1}{\overset{N}{G_{m}\sum}}{a_{n}^{2}.}}}$The array receiving system may be represented by an equivalent singleantenna with output P_(o)G_(a) and a two-port receiver with

$G_{rec} = {{G_{m}{\sum\limits_{n = 1}^{N}a_{n}^{2}}} = {\sum\limits_{n = 1}^{N}{G_{n}.}}}$The effective input noise temperature of the array receiver is

$T_{rec} = {\frac{\sum\limits_{n = 1}^{N}{G_{n}T_{n}}}{G_{rec}} = {\frac{\sum\limits_{n = 1}^{N}{G_{n}T_{n}}}{\sum\limits_{n = 1}^{N}G_{n}}.}}$The excess output noise density is N_(o)=kTG_(rec)+kT₀(1−G_(c)).Therefore, the noise temperature is

$T_{rec} = {T + {\frac{T_{0}}{G}{( {\frac{1}{G_{c}} - 1} ).}}}$

For downlink multi-beam coverage, we select the size of the n×n array,i.e., its gain and noise temperature in order to meet thefield-strengths,

${E = {\frac{\sqrt{30P_{T}G_{T}}}{r}{V/m}}},$according to Table 1 below, where the satellite array formationmaintains the same field strength from the satellite (above) as providedby terrestrial base stations use on cellular systems (below).

TABLE 1 Mobile System Average TIS [dBm] Electrical fieldstrength [mV/m]GSM900 −91.8 dBm 177 μV/m GSM1800 −93.7 dBm 277 μV/m UMTS900 −96.4 dBm104 μV/m UMTS2100 −99.6 dBm 163 μV/m

As best illustrated in FIG. 5, the control satellite 200 of eachsatellite formation 100 can handle beam-switching. For example, a givenregion (such as having a 400 km diameter) is designated with a beamindex corresponding to a particular set of longitudes and latitudes, andthe beams are mapped worldwide with each beam having a unique index.That information can be stored in memory at the control satellite 200.The control satellite 200 (for example based on its global positiondetermined from its GPS 202), determines which beam it should transmitto at any given time. In one preferred embodiment of the invention, eachbeam will only communicate with a single satellite formation 100.Accordingly, there is no overlap in beams, or minimal overlap, and thesatellite formations 100 will conduct beam-switching as the formations100 move into and out of a particular beam. To minimize beam switching,the satellite formation 100 assigned to a particular beam will be theformation 100 from the entire constellation of formations 100, thatcovers that beam location for the longest duration, i.e. period of time.The control satellites 200 can communicate their position to the othercontrol satellites 200 to facilitate the beam switching operation.

FIGS. 5(a)-5(c) depict communication protocol for beam-switching forpurposes of illustrating the invention. Three (fixed) multi-beamfootprints 400 are shown. Many fixed footprints tessellate (i.e., cover)the Earth, perhaps with some overlap between footprints. FIG. 5 shows asatellite formation 100 (which includes the control satellite 200 andthe array 300) as it orbits the Earth and approaches a footprint (FIG.5(a)), then passes over that footprint (FIG. 5(b)), and finally movesaway from that footprint (FIG. 5(c)). A first satellite formation 100provides communication coverage for given first multi-beam footprintuntil an adjacent multi-beam is nadir (immediately below the satellite).At this point, the first formation 100 switches to serving an adjacentsecond multi-beam footprint under it. Simultaneously, a rising secondformation switches its multi-beam footprint so as to provide continuouscoverage to the first multi-beam footprint. The beam-switching happensat the formation based on its ephemeris, i.e., when it starts to leavethe multi-beam footprint and another formation starts to serve themulti-beam footprint. The control satellite 200 can communicate theappropriate communication protocol (frequency, etc.) to the remotesatellites 302. Though beam-switching is described as being performed bythe control satellite 200, it can be performed by one or more of theremote satellites 302.

The control satellite 200 commands the remote satellites 302 by sendingthem the beamforming coefficients. The controller satellite 200, atKa-band or higher frequency, is based on the aggregation of array's 300beams. The aggregation of all beams must be communicated by the controlsatellite to the Ground Station (and thence the network cloud) via itshigh-frequency downlink, while it distributes data uplinked to it in Kaband to the various very small satellites for communication to thehand-sets.

Turning to FIG. 6, an array 500 is shown in accordance with analternative embodiment of the invention. The array 500 is formed by thesmall satellites 302 being positioned in a trapezoidal configurationsubstantially having the shape of a frustrum of a pyramid with a bottomarray 502 and side arrays 504 a-504 d. That is, the bottom array 502 isformed by small satellites 302 e positioned in rows and columns alongthe tracks of ellipses to form a bottom array 502 of satellites. Andeach of the side arrays 504 a-504 d (front side array 504 a, right sidearray 504 b, rear side array 504 c, and left side array 504 d) areformed by the small satellites 302 being positioned in rows and columnsalong the tracks of ellipses orthogonal to the radio of the earth.

Several small satellites 302 c, 302 d, 302 e are shown in FIG. 6 toillustrate the trapezoidal array 500, though it will be recognized thatthe entire trapezoidal array 500 is comprised of small satellites 302positioned along the bottom 502 and sides 504 of the array 500. Forexample, the side array 504 c is formed by small satellites 302 c beingformed in columns and rows along the tracks of ellipses orthogonal tothe radios of the earth and the side array 504 d is formed by smallsatellites 302 d being formed in columns and rows along the track ofellipses orthogonal to the radios of the earth. The bottom array 502 canbe substantially square or rectangular or an ellipse and the side arrays504 can each substantially have an isosceles trapezoid shape. Thus, theside arrays 504 a-504 d are angled outwardly from the planar surface ofthe bottom array 502, and can either be adjacent to each other or spacedapart. Notably though, each of the arrays 502, 504 a-504 d aresubstantially orthogonal to the radius of the earth.

As further illustrated in FIG. 6, the small satellites 302 are allpositioned in the same forward-facing direction 510, which issubstantially perpendicular to the planar surface of the bottom array502. That is, the small satellites 302 are of any shape and have aforward-facing top planar surface. The top surface faces in thedirection 510 of the earth, whereby planar surfaces of the remotesatellites are substantially orthogonal to the surface of the earth(i.e., orthogonal to the radius of the earth). The array is positionedto cover the nadir areas. For a large footprint, the nadir beam is notdirectly looking at other domains of the footprint. In order to coverthese regions, we provide four more faces, inclined to the nadir plane.

The trapezoid or any equivalent volumetric figure array 500configuration addresses the signals to the region directly, or nearlyso, so that the cosine loss is manageable the signals transmittedto/from the Earth ground station, and reduces cosine losses. The controlsatellite 200 is located at the center of mass of the array 500. The“cosine loss” is the cosine of the angle of the normal to the plane tothe line joining the center of the plane to the region being looked at.Since cosine is always less than or equal to 1, it is always a loss andnever a gain, and the more the angle, the greater the loss. Theadditional planes to 502, 504 a-d, in FIG. 6 of the trapezoid areprovided to reduce that loss.

It is further noted that the bottom 502 and sides 504 are shown as flathaving planar dimensions and angled corners where they intersect. Itshould be noted that the shape can be more curved, with curveddimensions and curved corners as form by an ellipse. And otherconfigurations of the array can be provided having different arrayshapes, including three-dimensional shapes or polymetric shapes. Inaddition, the array 500 can be oriented with respect to the Earth in anysuitable manner to point to either earth 510 or space 512.

FIGS. 7(a)-7(c) show Ephemeris-based beam-to-sub-formation assignmentuse on a broadband communications applications of the invention, whereFIG. 7(a) shows the formation entering the footprint on Earth, FIG. 7(b)shows the formation in the middle of the footprint, and FIG. 7(c) showsthe formation leaving the footprint. The boundaries in the footprintshow the sub-formation being used to cover the beams. Here, beam Tx andRx are switched to/from the selected formation. The switch may becommunicated by the central satellite 200. The figures shows thesatellite transit of footprint centre, but off-center footprint transitis possible as well. The figure illustrates the assignment of beams tothe various faces of the frustum as the formation passes over thefootprint. It also illustrates that not all active faces of the frustumare necessarily active at any given time.

FIGS. 8(a), 8(b) show an alternative communication protocol to FIGS. 5,7 as a further non-limiting example of a beam switching operation. InFIG. 8(a) (as in FIGS. 5, 7), the entire earth is mapped into numerousbeams 450 and assigns each beam a unique beam index. That informationcan be stored in memory at the control satellites 200. The satelliteformation 100 is shown in orbit 102 around the earth. As the formation100 travels in orbit 102, its footprint 104 moves along the surface ofthe earth, whereby the satellite formation 100 can communicate with thebeams 450 that are inside its footprint 102. Thus, as the satelliteformation orbits the earth, the footprint 104 of the satellite formation100 moves from the position shown in FIG. 8(a) to the position shown inFIG. 8(b). In addition, referring to FIG. 8(c), there can be multiplesatellite formations 100 in a single orbit 102. As illustrated in FIG.8(c), six satellite formations 100 (three are shown on the half of theearth that is illustrated) can be in a single orbit 102. The footprints104 of the satellite formations 100 do not overlap with each other.

Each beam 450 is uniquely allocated to only one satellite formation 100based on the latitude and longitude of the beam 450 and the position ofthe satellite formation 100. When multiple satellite formations 100 canservice a beam 450, the beam 450 can be allocated to a satelliteformation 100 that can provide coverage for the longest duration.

FIGS. 9(a), 9(b) show radiation patterns (a radiation pattern is theantenna array gain as a function of its angle from the array'sboresight) for a 64×64 element array and 16×16 element array,respectively. One possible patch (or printed-circuit board) antenna sizeis 80 mm×80 mm×2 mm, the element spacing is 166 mm, and the frequency is700 MHz. A patch antenna one type of antenna that can be realized on aPCB. There are several other types, such as microstrip etc., that can berealized on a PCB. The composite radiation pattern of a 64×64 antenna isdepicted. What is shown is the narrow main lobe and much smallersurrounding sidelobes. It may be one design choice to select the angleof the frustum so that one array is in another's null. The radiationpattern also shows where the nulls are.

Turning to FIG. 10, frequency assignment is shown for the footprint ofthe array 300, for the transmit and receive frequencies Tx, Rx (whichcan communicate on a same band, but different frequencies). The 4-colorconfiguration is shown, where each color represents a differentfrequency. Thus, only four colors (i.e., frequencies) are needed tocolor any 2-dimension map in such a way that no two adjacent cells havethe same frequency. If the beams are hexagonal cells, then only 4frequencies suffice (and they are regular with alternation of 2frequencies on one row and an alternation of 2 other frequencies on thenext, alternating the rows). Thus, frequency reuse factor may optimallybe 4. However, even when the interference is restricted to adjacentcells, it has been shown that the problem of optimal coloring of theinterference graph G is NP-complete. Several approximation algorithmshave been devised for fixed assignments. Fixed Allocation (FA) uses nomore than three times the optimal number of frequencies (or colors). Wetake frequency reuse factor of 7, bearing in mind that it could bebrought down to 4 (since satellite beams closely follow a hexagonal gridand interference skipping one cell is small). The four frequencies canaccommodate b beams (e.g., 500). Assuming each beam b can handlebandwidth bw, then the entire throughput will be b×bw for each cell. Ofcourse, any suitable number of frequencies and footprint cells can beprovided, more or less than four.

Delay and Doppler Pre-Compensation by Formation is performed at thecentral satellite 200. The satellite formation, knowing its ephemeris,pre-compensates delay and doppler variations to the center of each beamof the footprint it is serving, so as to minimize the residual Dopplerseen by a handset anywhere within that beam and so that the delay seenby the handset is as close to a constant delay as possible. ResidualDoppler and delay variations, after pre-compensation for the center ofthe beam (as a function of the formation ephemeris with respect to thecenter of each beam). As a consequence, the hand-phone will see delayand Doppler variations at off-center locations, but these will be small(of the order of three times what might be observed in a terrestrialbase-station service).

Alternatively, these delay and Doppler compensation could equally bemade at the ground station (GS), such as a virtual Base-Station, asshown in FIG. 11. This is combined with the large aperture anddelay/Doppler compensation to the beam-center. The larger the aperture,the smaller the (worst-case) residual Doppler (after residual Dopplercompensation) in the beam. LTE does not tolerate residual Doppler>1200Hz nor delay variations>0.5 ms. So, a) there has to be delay/Dopplercompensation/equalization and b) the residual delay/doppler variationsmust be small. The method of compensation at the ground station can bethe same as the compensation done at the satellite.

FIG. 11 shows the organization of equipment at the ground station (GS)700 that generate the various beam signals and transmit to the LEOformation 100 and receive the various beam signals from LEO formation100. The virtual base-stations 702, 704, . . . , 706 are N base-stationsthat generate/receive the signals to/from the handsets in N beams ofsatellite footprint through the LEO formation 100. Each base-stationtransmitted/received signal goes through a delay/Doppler compensationaided by inputs from the GPS module 712, LEO constellation ephemerismodule 716, ground station and beam frequency module 710, and beam tobase-station map or beam geo-location and schedule module 714. The GPSmodule 712 provides the location co-ordinates of the ground station 700,and the LEO Constellation ephemeris 716 provides the LEO formation 100co-ordinates. The ground station and beam frequencies module 710provides a list of the ground station uplink/downlink frequency assignedto each base-station to/from the LEO formation 100 and correspondinguplink/downlink frequency assigned to each beam in the satellitefootprint to/from the LEO formation 100. The beam to base-station mapand schedule module 714 lists which beam is assigned to whichbase-station and the time instances when a base-station startsgenerating/receiving a signal to/from the beam and when it is stopped.

The inputs 710, 712, 714, 716 aid in computing the delay/Doppler trendwell ahead of the satellite passes over the beam. For Dopplercompensation, when the satellite pass starts over the beam, the inverseDoppler is applied to the virtual base-station generated signal thatcancels Doppler effect due to LEO formation movement in the forwarddirection (from Ground station to LEO formation to User Equipment)resulting in near zero Doppler as seen by the end User Equipment.Similarly, the inverse Doppler is applied on the downlink from LEOformation prior to feeding to virtual base-station to cancel the Dopplereffect in the reverse direction (from User Equipment to LEO formation toGround station).

The compensation is updated periodically to adapt to the Doppler changesduring the satellite pass and is carried out till the end of thesatellite pass. For delay compensation, a finite latency exists betweenthe Ground Station and the User Equipment as signals are exchangedbetween them via LEO formation depending on the path delay from theGround Station and User Equipment to LEO formation. Since this delaycannot be reversed, the delay compensation involves adding aproportionate delay such that overall delay is near constant throughoutthe satellite pass between Ground Station and User Equipment.

For example, let us assume the Ground Station and the User Equipment arein the same beam. When the beam is at the edge of the LEO formationfootprint, the path delay is large (say d₁) and the corresponding delayadded (say cd₁) for compensation is at a minimum. Similarly, when thebeam is at nadir (below the LEO formation) during the satellite pass,the path delay is minimum (say d₂) and the corresponding delay added(say cd₂) for compensation is at a maximum. For these illustratedscenarios, though the path delay varied depending on the beam positionin the LEO formation footprint, the overall path delays are nearlyconstant, i.e., (d₁+ cd₁)≈(d₂+ cd₂). Thus, the invention provides adynamic and variable delay based on the existing path delay, to achievea nearly constant final resulting path delay as the satellite travels.

So, the delay/Doppler compensation mechanisms aid in maintaining nearconstant path delay and near zero Doppler (i.e., equalized) betweenvirtual base-stations and the User Equipment required to establishcommunication between them despite having a LEO formation channelbetween them. Here, near zero Doppler and near constant delay meansDoppler and delay variation that does not disrupt or severely degradeLTE communications. For fixed terrestrial services, in one embodimentthey are within ±800 Hz, ±0.2 ms and for airborne mobile services within±1100 Hz, ±0.3 ms.

Likewise, the virtual base-stations communicating with other beams andvirtual base-stations at other ground stations also maintain a nearconstant path delay and near zero Doppler for the respective LEOformations in constellation. Since the overall path delay/Doppler ismaintained to be near similar across beams and across LEO formations,the User Equipment quickly synchronize to new beams whenever there istransition of a User Equipment between beams or transition of a beamfrom a setting LEO formation footprint to a rising LEO formationfootprint, thereby providing a smooth transition from satellite tosatellite of User Equipment.

All these inputs are obtained over a local area network or over a cloudfrom the remote network 708. The signals of each base-station 702, 704,. . . , 706 could be a common LTE band frequency (ƒ), they areinterleaved/de-interleaved in frequency to/from (ƒ₁, ƒ₂, . . . , ƒ_(N))using frequency division multiplexer/de-multiplexer 720. The compositesignal of all base-stations from/to the multiplexer/de-multiplexer 720is then frequency shifted to/from a leased satellite frequency band(like Q or V-band) by the base-station frequency to satellite frequencyup/down converter 722. The ground station antenna 724 transmits/receivesthe composite base-station signals to/from the LEO formation 100.

As described above, a central satellite 200 is utilized to controloperation of the remote satellites 302, such as to control formation,i.e., positioning of the small satellites 302 to form the satellitearray 300, 500, including spacing between the respective remotesatellites 302. It should be noted, however, that remote satellites 302(i.e., the remote controller 304) can communicate with one another toperform certain operations, including formation of the satellite array300, 500, instead of or in addition to utilizing the central satellite200. Still other components can be provided in the remote satellites302, such as a proximity detector or sensor, to facilitate formation ofthe remote satellites 302 to achieve a predetermined or dynamic positionbetween the remote satellites 302. Formation of the array can bepredefined or dynamically adjusted.

The large antenna array 300, 500 effectively operates as a large antennafor the control satellite 200, which itself is a small satellite. Assuch, the antenna array 300, 500 enables enhanced communication betweenthe control satellite 200 and the Earth. Accordingly, the controlsatellite 200 can transmit and receive signals directly to low-poweredantenna devices, such as cell phones or the like.

In yet another embodiment of the invention, the phase array 300, 500 canbe utilized to collect solar energy from the sun. For example, thesatellites 302 or satellite modules can be made from photovoltaicmaterial or other material that converts solar energy to electricalenergy to operate as a solar panel, and also operate as an antennastructure (or other structure of the satellite or satellite module) totransmit and receive signals in accordance with the invention. Theelectrical energy is used to power the satellite 302 or satellitemodules or stored for later use. Thus, the same structure can be usedfor solar energy and for operation as a satellite antenna.

In addition, the invention can be used to support ground virtual eNodeBto compensate for large delay and support standard devices in 2G, 3G,4G, and 5G. In more detail, in order for the invention 100 tocommunicate with end user devices on the ground such as mobile devices,it utilizes Doppler compensation and equalized delay. Yet, standardcommunication protocols are only capable of handling communications insystems where transmissions are received quickly with small delays, suchas within 0.66 ms. But in the present invention, there is a largecommunication delay between the remote satellites or satellite modulesand the end user devices. That large transmission delay creates errorswhen sending signals according to standard communication protocols. So,the invention utilizes a communication protocol to allow for seamlesscommunication despite large transmission delays across 2G, 3G, 4G and 5Gsystems, such as shown and described in U.S. Provisional Application No.62/758,217 filed Nov. 9, 2018, and the non-provisional application Ser.No. 16/379,399, filed Apr. 9, 2019, now U.S. Pat. No. 10,841,890, theentire contents of which is hereby incorporated by reference. Thecombination of Doppler compensation, equalized delay, and adelayed-transmission communication protocol, enables seamless,continuous and reliable communication between the remote satellites 302or satellite modules and user ground devices. The protocol can beimplemented at the ground station and/or at the satellite or satellitemodule.

As further described above, the remote satellites 302 or satellitemodules can be moved into position and retained in position by using,for example, electromagnetic forces. Still further, the remotesatellites 302 or satellite modules can be moved into position or heldin position by mechanical devices. For example, the remote satellites302 or satellite modules can physically engage each other to createmovement, and can be mechanically engaged or attached to one another aseach remote satellite moves into its final operating position. Forexample, the remote satellites 302 or satellite modules can be coupledtogether by a mechanical mechanism such as a hinge or the like thatrotatably connect the satellites to pivot or rotate about the mechanismwith respect to one another. Thus, the connected satellites 302 orsatellite modules can be folded onto each other into a small compactstorage or transport configuration, and then mechanically unfolded intoa large operating configuration.

Each remote satellite 302 or satellite module can be, for example, amicro satellite or antenna that is mechanically and rotatably coupled toat least one neighboring satellite 302 or satellite module. Each remotesatellite 302 or satellite module can have multiple neighboring remotesatellites 302 or satellite modules, such as four on each side andpossibly one above, below and at diagonals. Each remote satellite orsatellite module can have a mechanical mechanism or device connecting itto at least one of its neighboring remote satellites or modules in amanner that provides an efficient folding of the remote satellites orsatellite modules into a compact storage configuration. It is furthernoted that the remote satellites or modules can be connected in othersuitable manners to permit rotation or other relational movement, suchas for example sliding, pivoting, extending, collapsing.

It is further noted that the term “satellite” and/or “satellite module”are generally interchangeably used to describe the remote satellites 302as an element, object or device that can be placed into space. Thoughthe preferred embodiment is described above as including a processor304, receiver(s)/transmitter(s), and up to four antenna 305, otherembodiments need not include each of those components. Moreover, in oneembodiment, the satellite or satellite module can comprise just one ofthose components. For example, the satellite or satellite module can bean antenna, a portion of an antenna, or any other element, object,device or component that is placed into space, typically to support, forexample, communication with other satellites, ground station, and/or enduser device.

In the embodiment of FIGS. 1-2, the remote controller and/or the centralcontroller can include a processing device to perform various functionsand operations in accordance with the invention, including at the groundstation 700 and the inputs 710-716 to the base stations 702-706. Theprocessing device can be, for instance, a computing device, processor,application specific integrated circuits (ASIC), or controller. Theprocessing device can be provided with one or more of a wide variety ofcomponents or subsystems including, for example, a co-processor,register, data processing devices and subsystems, wired or wirelesscommunication links, and/or storage device(s) such as memory, RAM, ROM,analog or digital memory or database. All or parts of the system,processes, and/or data utilized in the invention can be stored on orread from the storage device. The storage device can have stored thereonmachine executable instructions for performing the processes of theinvention. The processing device can execute software that can be storedon the storage device. Unless indicated otherwise, the process ispreferably implemented in automatically by the processor substantiallyin real time without delay.

The description and drawings of the present invention provided in thepaper should be considered as illustrative only of the principles of theinvention. The invention may be configured in a variety of ways and isnot intended to be limited by the preferred embodiment. Numerousapplications of the invention will readily occur to those skilled in theart. Therefore, it is not desired to limit the invention to the specificexamples disclosed or the exact construction and operation shown anddescribed. Rather, all suitable modifications and equivalents may beresorted to, falling within the scope of the invention.

The invention claimed is:
 1. A communication system comprising: a groundstation for transmitting and receiving signals to and from a satelliteor satellite formation, said ground station configured to apply aninverse Doppler to cancel Doppler effect on the signals to provide anequalized near-zero Doppler, wherein the satellite or satelliteformation corresponds to a plurality of beams each pre-compensated tothe center of the beam and has an aperture adjusted to such a large sizethat pre-compensated residual Doppler and delay variations at off-centerlocations in each beam with respect to the center of the beam are withinlong-term-evolution (LTE) and other 3GPP standards.
 2. The communicationsystem of claim 1, wherein the signals having a path delay, said groundstation further configured to apply a variable delay based on the pathdelay to provide an equalized final constant path delay for the signals.3. The system of claim 2, wherein the overall delay induced by theground station at each beam-center is a constant.
 4. The system of claim1, said ground station configured to provide a delayed-transmissioncommunication protocol to account for communication delay between saidground station and the satellite or satellite formation.
 5. The systemof claim 1, said satellite or satellite formation configured to providea delayed-transmission communication protocol to account forcommunication delay between said satellite or satellite formation andsaid ground station and/or ground user devices.
 6. The system of claim1, wherein said ground station forms a beam with the satellite orsatellite formation, wherein the beam is pre-compensated based onsatellite ephemeris and beam-center latitude-longitude, for Dopplerfrequency shift induced by the satellite or satellite formation.
 7. Thesystem of claim 1, said ground station forming a beam with the satelliteor satellite formation, wherein the beam is pre-compensated based onsatellite ephemeris and beam-center latitude-longitude, for Dopplerfrequency shift induced by the satellite or satellite formation.
 8. Thesystem of claim 7, further comprising a plurality of virtualbase-stations and a down converter receiving a composite signal from thesatellite or satellite formation and providing a down-converted signal.9. The system of claim 8, further comprising a demultiplexer receivingthe down-converted signal and providing a demultiplexed down-convertedsignal to each of the plurality of virtual base-stations.
 10. The systemof claim 1, further comprising a plurality of virtual base-stations anda frequency division multiplexer receiving a signal from each of saidplurality of virtual base-stations to form a composite signal.
 11. Thesystem of claim 10, further comprising an up converter receiving thecomposite signal from said frequency division multiplexer andtransmitting an up-converted composite signal to the satellite orsatellite formation.
 12. The system of claim 1, wherein the aperture isadjusted to have such a large size that the pre-compensated residualDoppler at off-center locations in each beam with respect to the centerof the beam is within 1200 Hz.
 13. The system of claim 1, wherein theaperture is adjusted to have such a large size that the pre-compensateddelay variations at off-center locations in each beam with respect tothe center of the beam are within 0.1 ms.